simplify \\( \\frac{\\sin ^{2}(t)+\\cos ^{2}(t)}{\\sin ^{2}(t)} \\) to an expression involving a single trig…
simplify \\( \\frac{\\sin ^{2}(t)+\\cos ^{2}(t)}{\\sin ^{2}(t)} \\) to an expression involving a single trig function with no fractions.
Answer
Explanation:
Step1: Use the Pythagorean identity
We know that (\sin^{2}(t)+\cos^{2}(t) = 1). So the expression becomes (\frac{1}{\sin^{2}(t)}).
Step2: Use the reciprocal identity
Since (\csc(t)=\frac{1}{\sin(t)}), then (\frac{1}{\sin^{2}(t)}=\csc^{2}(t)).
Answer:
(\csc^{2}(t))